Question

Coefficient of x in the expansion of $\left( \sum_{k = 1}^{n}a_{k} \right)^{2} =$ is.

• A. $\left( \frac{n}{n + 1} \right)^{2}$
• B. $\left( \frac{n}{n + 1} \right)^{4}$
• C. $\left( \frac{n}{n + 1} \right)^{6}$
• D. $(1 + x)^{5}$

Answer 1

Answer: (B)

$\left( \frac{n}{n + 1} \right)^{4}$

Answer 2

In the expansion of $\therefore D^{r} = 3^{6} +^{6}C_{1}3^{5}.2^{1} +^{6}C_{2}3^{4}.2^{2}$ the general term is

$(3 + 2)^{6}$

Here, exponent of x is $= 5^{6} = (25)^{3}$

$\therefore\frac{N^{r}}{D^{r}} = \frac{(25)^{3}}{(25)^{3}} = 1$ $(1 + x)^{n}$

Hence coefficient of x is $(r + 1)osa,(r + 2)osa,(r + 3)osa$.